Exercise 4.6-1

Give a simple and exact expression for \(n_j\) in equation (4.27) for the case in which \(b\) is a positive integer instead of an arbitrary real number.

Equation 4.27 is

\[n_j = \begin{cases} n & \text{if } j = 0 \text{,} \\ \lceil n_{j-1}/b\rceil & \text{if } j > 0 \text{.}\\ \end{cases}\]

If \(b\) is a positive integer, we can simplify this expression to be \(n_j = \lceil n/b^j \rceil\).